Which of the following best describes a nonlinear association in a scatterplot?

• A. The points form a straight line with a $\mathrm{negative}\mathrm{slope}$.
• B. The points form a straight line with a $\mathrm{positive}\mathrm{slope}$.
• C. The points are randomly scattered with no apparent pattern.
• D. The points form a curved pattern, such as a $\mathrm{parabola}$ or $\mathrm{exponential}$ shape.

Answer: (D)

Verified step by step guidance

1. Understand that a scatterplot displays the relationship between two quantitative variables by plotting data points on a coordinate plane.
2. Recall that a linear association means the points roughly form a straight line, which can have a positive slope (increasing) or a negative slope (decreasing).
3. Recognize that a nonlinear association occurs when the points do not align along a straight line but instead form a curved pattern, such as a parabola, exponential curve, or other shapes.
4. Identify that if the points are randomly scattered with no apparent pattern, this indicates no association rather than a nonlinear association.
5. Conclude that the best description of a nonlinear association is when the points form a curved pattern, distinguishing it clearly from linear or no association.